Question

4 step process of using heat to generate electricity.

A to B: Isotherm Th; adds heat under pressure to turn water to steam at 550K

B to C: Adiabatic expansion; Uses the steam to turn a turbine

C to D: Condenses the steam into water at 400K

D to A: Adiabatic compression; a 1.6 MW pump pushes the water to the boiler

When running at 75% of the peak Carnot efficiency, the plant produces 2.5 MW. Solve the chart below.

Path	Q	W	U
A to B
B to C
C to D
D to A
Total

Delta U = Q-W

Answer 1

Peak Carnot efficiency is:

e = 1 - T/T' = 1 - (400/550) = 0.2727 = 27.27%

actual efficiency = 0.2727 x 0.75 = 0.2045

Energy produced/s = W = 2.5 MW

Therefore, Q_h = 2.5 x 10⁶/0.2045 = 12.22 MW

from A to B: U = 0 [change in internal energy is zero]

Q = Q_h = 12.22 MW and from 1st Law of Thermodynamics, W = - Q = -12.22 MW

[work done by the gas]

From B to C,

Q = 0 [no heat transfer]

so, U = W = - 1.6 MW

C to D:

Q = Q_c = Q_h - W = 12.22 - 2.5 = 9.72 MW

U = 0

and W = - Q = - 9.72 MW

D to A:

W = U = 1.6 MW

Q = 0

Total: W = Q_h - Q_c = 2.5 MW, U = 0 and Q = Q_h = 12.22 MW.